GRAPHING POLYNOMIALS

By Noureen Villamar Melissa Motieram Elizabeth Stasiak

Period B

DEFINITIONS Polynomial-can have constants, variables and

exponents, but never division by a variable. Multiplicity- the number of times a root of an

equation or zero of a function occurs when there is more than one root or zero.

Minimum -the minimum value of a quadratic function; the lowest turning point.

Maximum - the maximum value of a quadratic function; the highest turning point.

X-intercept- where the graph crosses the x-axis Y-intercept- where the graph crosses the y-axis

STEPS FOR GRAPHING POLYNOMIALS

Find real zeros. (look for multiplicity)

- even multiplicity – touch x-axis.

- odd multiplicity – through x-axis. Use synthetic division to show that zeros are

factors. Test interval behavior (end behavior depends

on degree).

- even degree – same direction

- odd degree – different direction Number of turning points – maxima and

minimum.

- n-1=degree-1 Test intervals – sign analysis. Graph polynomial, include y- intercept.

EVEN DEGREE POLYNOMIAL Example:

ODD DEGREE POLYNOMIAL Example: